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 A324851 Numbers > 1 divisible by the sum of their prime indices. 14
 2, 4, 6, 12, 15, 16, 20, 30, 35, 36, 42, 48, 56, 88, 99, 112, 120, 126, 130, 135, 143, 144, 160, 162, 180, 192, 210, 216, 220, 221, 228, 231, 242, 250, 256, 270, 275, 280, 288, 297, 300, 308, 322, 330, 338, 360, 396, 400, 408, 429, 435, 440, 455, 468, 480, 493 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The sum of prime indices of n is A056239(n). For example, the prime indices of 99 are {2,2,5}, with sum 9, a divisor of 99, so 99 is in the sequence. For any k>=2, let d be a divisor of k such that d > A056239(k).  Then 2^(d-A056239(k))*k is in the sequence.  Similarly if k is in the sequence with d = A056239(k), then 2^d*k is in the sequence. - Robert Israel, Mar 19 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE The sequence of terms together with their prime indices begins:     2: {1}     4: {1,1}     6: {1,2}    12: {1,1,2}    15: {2,3}    16: {1,1,1,1}    20: {1,1,3}    30: {1,2,3}    35: {3,4}    36: {1,1,2,2}    42: {1,2,4}    48: {1,1,1,1,2}    56: {1,1,1,4}    88: {1,1,1,5}    99: {2,2,5}   112: {1,1,1,1,4}   120: {1,1,1,2,3}   126: {1,2,2,4}   130: {1,3,6}   135: {2,2,2,3} MAPLE filter:= proc(n) local t; n mod add(numtheory:-pi(t[1])*t[2], t=ifactors(n)[2]) = 0 end proc: select(filter, [\$1..1000]); # Robert Israel, Mar 19 2019 MATHEMATICA Select[Range[2, 100], Divisible[#, Plus@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>PrimePi[p]*k]]&] PROG (PARI) isok(n) = {my(f = factor(n)); (n!=1) && !(n % sum(k=1, #f~, primepi(f[k, 1])*f[k, 2])); } \\ Michel Marcus, Mar 19 2019 CROSSREFS Cf. A003963, A036844, A056239, A112798, A120383, A290822, A306844. Cf. A324695, A324741, A324743, A324847, A324756, A324758, A324765, A324847, A324848, A324849, A324850, A324852. Sequence in context: A057830 A013916 A141113 * A334156 A255001 A050584 Adjacent sequences:  A324848 A324849 A324850 * A324852 A324853 A324854 KEYWORD nonn AUTHOR Gus Wiseman, Mar 18 2019 STATUS approved

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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)